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Telephone number (mathematics)

In the mathematics of chess, the telephone numbers count the number of ways to place rooks on an chessboard in such a way that no two rooks attack each other (the so-called eight rooks puzzle), and in such a way that the configuration of the rooks is symmetric under a diagonal reflection of the board.

Version
v1 · 2026-09-28 · History
Domain-specific #
12480
Domain group
Formal Sciences
Origin domain
Mathematics
Subdomains
Enumerative Combinatorics, Integer Sequences → Mathematics

Core Idea

Telephone number (mathematics) is treated here as the recurring crossdomainmodelsstructuresrepresentations identity summarized by this source-grounded definition: In the mathematics of chess, the telephone numbers count the number of ways to place rooks on an chessboard in such a way that no two rooks attack each other (the so-called eight rooks puzzle), and in such a way that the configuration of the rooks is symmetric under a diagonal reflection of the board. has ten matchings, corresponding.

Scope of Application

  • The exponential generating function of the telephone nu. In other words, the telephone numbers may be read off as the coefficients of the Taylor series of and, in particular, the -th telephone number is the value at zero of.

  • The exponential generating function of the telephone nu. The exponential generating function can be derived in a number of ways; for example, taking the recurrence relation for above, multiplying it by , and summing over gives.

  • The exponential generating function of the telephone nu. This function is closely related to the exponential generating function of the Hermite polynomials, which are the matching polynomials of the complete graphs.

  • Applications. John Riordan provides the following explanation for these numbers: suppose that people subscribe to a telephone service that can connect any two of them by a call, but cannot make a.

  • Applications. For instance, with three subscribers, there are three ways of forming a single telephone call, and one additional pattern in which no calls are being made, for a total of four.

Clarity

A clear use of Telephone number (mathematics) names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In the mathematics of chess, the telephone numbers count the number of ways to place rooks on an chessboard in such a way that no two rooks attack each other (the so-called eight rooks puzzle), and in such a way that.

Manages Complexity

Telephone number (mathematics) compresses multiple crossdomainmodelsstructuresrepresentations details into a stable diagnostic relation. The source shows both the central mechanism—a standard Young tableau is formed by placing the numbers from 1 to into these squares in such a way that the numbers increase from left to right and from top to bottom throughout the tableau.—and the practical consequence—first published in 1800 by Heinrich August Rothe, by which they.

Abstract Reasoning

  1. Type the carrier. Identify the crossdomainmodelsstructuresrepresentations entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: In the mathematics of chess, the telephone numbers count the number of ways to place rooks on an chessboard in such a way that no two rooks attack each other (the so-called eight rooks puzzle), and in such a way that the configuration of the rooks is symmetric under a diagonal reflection of.

Knowledge Transfer

Within the home domain. Knowledge about Telephone number (mathematics) transfers literally when a new case preserves the same carrier type, relation, and recognition test. In other words, the telephone numbers may be read off as the coefficients of the Taylor series of and, in particular, the -th telephone number is the value at zero of the -th derivative of this function. The exponential generating function.

Neighborhood in Abstraction Space

Telephone number (mathematics) sits in a sparse region of the domain-specific corpus (66th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (2551 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08